Question

how to solve tiz???


I'll mark BRAINLIEST
if u giv the right answer ​

Answer 1

Answer:

$\sf{D=4r^2}$

Step-by-step explanation:

$\sf{Consider\:the\:quadratic\:equation\:ax^2+bx+c=0}$

$\sf{where\:a,b,c\:\epsilon\:R\:and\:a\:\neq\:0}$

$\sf{Roots\:of\:the\:equation\:are\:given\:by}$

$\sf{x=\dfrac{-b+\sqrt{b^2-4ac}}{2a}}$

$\sf{The\:nature\:of\:roots\:depends\:upon\:b^2-4ac}$

$\sf{This\:quantity\:is\:generally\:denoted\:by\:D\:and}$

$\sf{is\:known\:as\:the\:discriminant\:of\:the\:quadratic}$

$\sf{equation.}$

$\sf{Given\:equation\:is}$ $\sf{x^2-2x-(r^2-1)}$

$\sf{D=b^2-4ac}$

$\sf{D=(-2)^2-4(-1)(-(r^2-1))}$

$\sf{D=4+4r^2-4}$

$\boxed{\sf{D=4r^2}}$

Answer 2

Discriminant of quadratic equation is $\mathbf{4r^{2}}$

Step-by-step explanation:

• Given data

       Quadratic equation is

       $\mathbf{x^{2}-2x-(r^{2}-1)=0}$     ...1)

• On comparing above quadratic equation to standard equation $\mathbf{ax^{2}+bx+c=0}$             ...2)

• So on comparing respective quantity of equation 1) , equation 2)

        a = 1

        b = -2

        $\mathbf{c = -(r^{2}-1)}$

• We know the formula of discriminant

        $\mathbf{D =b^{2}-4ac}$                 ...3)

• On putting respective value in equation 3)

        $\mathbf{D =(-2)^{2}-4\times 1\times \left [ -(r^{2}-1) \right ]}$

        $\mathbf{D =4+4\times (r^{2}-1)}$

        $\mathbf{D =4+4r^{2}-4}$

        So

        $\mathbf{Discriminant =4r^{2}}$        Answer